Acronym ... Name 2srid (?) Circumradius sqrt[sqrt(5)+11/4] = 2.232951 Vertex figure 2[3,4,10/2,4] (type A) or 2[6/2,4,5,4] (type B) or 2[6/2,4,10/2,4] (type C) Snub derivation ` (type A)   (type B)   (type C)` General of army srid Colonel of regiment srid Confer non-Grünbaumian master: srid

Looks like a compound of 2 small rhombicosidodecahedra (srid), and indeed vertices, edges, and {4} coincide by pairs (type C). For type A additionally {3} resp. for type B additionally {5} coincide by pairs as well.

Incidence matrix according to Dynkin symbol

```β3β5x   (type A)

demi( . . . (a)) | 60  * |  1  2  0  1 |  1  0  1  2
demi( . . . (b)) |  * 60 |  1  0  2  1 |  0  1  1  2
-----------------+-------+-------------+------------
both( . . x    ) |  1  1 | 60  *  *  * |  0  0  1  1
sefa( s3s . (a)) |  2  0 |  * 60  *  * |  1  0  0  1
sefa( s3s . (b)) |  0  2 |  *  * 60  * |  0  1  0  1
sefa( . β5x    ) |  1  1 |  *  *  * 60 |  0  0  1  1
-----------------+-------+-------------+------------
s3s . (a)  ♦  3  0 |  0  3  0  0 | 20  *  *  *
s3s . (b)  ♦  0  3 |  0  0  3  0 |  * 20  *  *
. β5x      ♦  5  5 |  5  0  0  5 |  *  * 12  *
sefa( β3β5x    ) |  2  2 |  1  1  1  1 |  *  *  * 60
```
```or
both( . . . ) | 120 |  1   2  1 |  1  1  2
--------------+-----+-----------+---------
both( . . x ) |   2 | 60   *  * |  0  1  1
sefa( s3s . ) |   2 |  * 120  * |  1  0  1
sefa( . β5x ) |   2 |  *   * 60 |  0  1  1
--------------+-----+-----------+---------
both( s3s . ) ♦   3 |  0   3  0 | 40  *  *
. β5x   ♦  10 |  5   0  5 |  * 12  *
sefa( β3β5x ) |   4 |  1   2  1 |  *  * 60

starting figure: x3x5x
```

```β5β3x   (type B)

demi( . . . (a)) | 60  * |  1  2  0  1 |  1  0  1  2
demi( . . . (b)) |  * 60 |  1  0  2  1 |  0  1  1  2
-----------------+-------+-------------+------------
both( . . x    ) |  1  1 | 60  *  *  * |  0  0  1  1
sefa( s5s . (a)) |  2  0 |  * 60  *  * |  1  0  0  1
sefa( s5s . (b)) |  0  2 |  *  * 60  * |  0  1  0  1
sefa( . β3x    ) |  1  1 |  *  *  * 60 |  0  0  1  1
-----------------+-------+-------------+------------
s5s . (a)  ♦  5  0 |  0  5  0  0 | 12  *  *  *
s5s . (b)  ♦  0  5 |  0  0  5  0 |  * 12  *  *
. β3x      ♦  3  3 |  3  0  0  3 |  *  * 20  *
sefa( β5β3x    ) |  2  2 |  1  1  1  1 |  *  *  * 60
```
```or
both( . . . ) | 120 |  1   2  1 |  1  1  2
--------------+-----+-----------+---------
both( . . x ) |   2 | 60   *  * |  0  1  1
sefa( s5s . ) |   2 |  * 120  * |  1  0  1
sefa( . β3x ) |   2 |  *   * 60 |  0  1  1
--------------+-----+-----------+---------
both( s5s . ) ♦   5 |  0   5  0 | 24  *  *
. β3x   ♦   6 |  3   0  3 |  * 20  *
sefa( β5β3x ) |   4 |  1   2  1 |  *  * 60

starting figure: x5x3x
```

```x3β5x   (type C)

both( . . . ) | 120 |  1  1  1  1 |  1  1  1  1
--------------+-----+-------------+------------
both( x . . ) |   2 | 60  *  *  * |  1  0  1  0
both( . . x ) |   2 |  * 60  *  * |  0  1  1  0
sefa( x3β . ) |   2 |  *  * 60  * |  1  0  0  1
sefa( . β5x ) |   2 |  *  *  * 60 |  0  1  0  1
--------------+-----+-------------+------------
x3β .   ♦   6 |  3  0  3  0 | 20  *  *  *
. β5x   ♦  10 |  0  5  0  5 |  * 12  *  *
both( x . x ) |   4 |  2  2  0  0 |  *  * 30  *
sefa( x3β5x ) |   4 |  0  0  2  2 |  *  *  * 30

starting figure: x3x5x
```

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